Here is an extract from answer.com:

"phrasal verbs:

....

take up

1. To raise; lift.
2. To reduce in size; shorten or tighten: take up a gown.
3. To pay off (an outstanding debt, mortgage, or note).
4. To accept (an option, bet, or challenge) as offered.
5. To begin again; resume: Let's take up where we left off.
6. To use up, consume, or occupy: The extra duties took up most of my time.
7. To develop an interest in or devotion to: take up mountain climbing.
8. To deal with: Let's take up each problem one at a time.
9. To assume: took up a friendly attitude.
10. To absorb or adsorb: crops taking up nutrients.
11. To enter into (a profession or business): took up engineering."

I think #8 could fit.